Trigonometric sums in number theory and analysis:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English Russian |
| Published: |
Berlin
de Gruyter
2004
|
| Series: | De Gruyter expositions in mathematics
39 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. übers. |
| Physical Description: | X, 554 S. 25 cm |
| ISBN: | 3110162660 |
Staff View
MARC
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| 240 | 1 | 0 | |a Teorija kratnych trigonometričeskich summ |
| 245 | 1 | 0 | |a Trigonometric sums in number theory and analysis |c by G. I. Arkhipov ; V. N. Chubarikov ; A. A. Karatsuba |
| 264 | 1 | |a Berlin |b de Gruyter |c 2004 | |
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| 500 | |a Aus dem Russ. übers. | ||
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| 700 | 1 | |a Čubarikov, Vladimir N. |e Verfasser |4 aut | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface v
Basic Notation vii
Introduction 1
1 Trigonometric integrals 6
1.1 One dimensional trigonometric integrals 6
1.2 Singular integrals in Tarry s problem and related problems 20
1.3 Multiple trigonometric integrals 30
1.4 Singular integrals in multidimensional problems 43
2 Rational trigonometric sums 48
2.1 One dimensional sums 49
2.2 Singular series in Tarry s problem and in its generalizations 59
2.3 Multiple rational trigonometric sums 73
2.4 Singular series in multidimensional problems 77
3 Weyl sums 79
3.1 Vinogradov s method for estimating Weyl sums 79
3.2 An estimate of the function G(n) 94
3.3 An analog of Waring s problem for congruences 97
3.4 A new p adic proof of Vinogradov s mean value theorem 104
3.5 Linnik s p adic method for proving Vinogradov s mean
value theorem 133
3.6 Estimate for Vinogradov s integral for k small relative to n2 136
4 Mean value theorems for multiple trigonometric sums 144
4.1 The mean value theorem for the multiple trigonometric sum
with equivalent variables of summation 144
4.2 The mean value theorem for multiple trigonometric sums
of general form 167
5 Estimates for multiple trigonometric sums 181
5.1 Theorems on the multiplicity of intersection of multidimensional
regions 181
5.2 Estimates for multiple trigonometric sums 200
x Contents
6 Several applications 210
6.1 Systems of Diophantine equations 210
6.2 Fractional parts of polynomials 228
7 Special cases of the theory of multiple trigonometric sums 235
7.1 Double trigonometric sums 235
7.2 r fold trigonometric sums 274
7.3 An asymptotic formula 312
8 The Hilbert Kamke problem and its generalizations 316
8.1 Study of the singular series in the Hilbert—Kamke problem 317
8.2 The singular integral in the Hilbert Kamke problem 343
8.3 Multidimensional additive problem 353
9 The p adic method in three problems of number theory 361
9.1 The Artin problem of finding a local representation of zero by a form 361
9.2 The p adic proof of Vinogradov s theorem on estimating G(n) in the
Waring problem 378
9.3 Fractional parts of rapidly growing functions 390
10 Estimates of multiple trigonometric sums with prime numbers 412
10.1 Some well known lemmas 413
10.2 Lemmas on estimates for multiple trigonometric sums with prime
numbers 416
10.3 The main theorem 441
10.4 Applications 447
10.5 On Vinogradov s problems in the theory of prime numbers 453
11 Some applications of trigonometric sums and integrals 469
12 Short Kloosterman sums 482
12.1 Mean value theorems 483
12.2 Analogs of incomplete Kloosterman sums and their estimates 489
12.3 Fractional parts of functions related to reciprocal values modulo
a given number 493
12.4 The function «*(«) and its mean value 502
12.5 Double Kloosterman sums 508
12.6 Short Kloosterman sums and their applications 513
Appendix 537
Bibliography 539
Index 553
|
| any_adam_object | 1 |
| author | Archipov, Gennadij I. 1945- Čubarikov, Vladimir N. Karacuba, Anatolij A. |
| author_GND | (DE-588)129604909 |
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| classification_rvk | SK 180 SK 450 |
| ctrlnum | (OCoLC)249618452 (DE-599)BVBBV019763183 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019763183 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:05:34Z |
| institution | BVB |
| isbn | 3110162660 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013089490 |
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| owner_facet | DE-824 DE-20 DE-634 DE-11 |
| physical | X, 554 S. 25 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Archipov, Gennadij I. 1945- Verfasser (DE-588)129604909 aut Teorija kratnych trigonometričeskich summ Trigonometric sums in number theory and analysis by G. I. Arkhipov ; V. N. Chubarikov ; A. A. Karatsuba Berlin de Gruyter 2004 X, 554 S. 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 39 Aus dem Russ. übers. Trigonometrisches Polynom Trigonometrisches Polynom (DE-588)4806392-7 gnd rswk-swf Trigonometrisches Polynom (DE-588)4806392-7 s DE-604 Čubarikov, Vladimir N. Verfasser aut Karacuba, Anatolij A. Verfasser aut De Gruyter expositions in mathematics 39 (DE-604)BV004069300 39 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013089490&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Archipov, Gennadij I. 1945- Čubarikov, Vladimir N. Karacuba, Anatolij A. Trigonometric sums in number theory and analysis De Gruyter expositions in mathematics Trigonometrisches Polynom Trigonometrisches Polynom (DE-588)4806392-7 gnd |
| subject_GND | (DE-588)4806392-7 |
| title | Trigonometric sums in number theory and analysis |
| title_alt | Teorija kratnych trigonometričeskich summ |
| title_auth | Trigonometric sums in number theory and analysis |
| title_exact_search | Trigonometric sums in number theory and analysis |
| title_full | Trigonometric sums in number theory and analysis by G. I. Arkhipov ; V. N. Chubarikov ; A. A. Karatsuba |
| title_fullStr | Trigonometric sums in number theory and analysis by G. I. Arkhipov ; V. N. Chubarikov ; A. A. Karatsuba |
| title_full_unstemmed | Trigonometric sums in number theory and analysis by G. I. Arkhipov ; V. N. Chubarikov ; A. A. Karatsuba |
| title_short | Trigonometric sums in number theory and analysis |
| title_sort | trigonometric sums in number theory and analysis |
| topic | Trigonometrisches Polynom Trigonometrisches Polynom (DE-588)4806392-7 gnd |
| topic_facet | Trigonometrisches Polynom |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013089490&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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